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Answer :

LlAestheticllgo

Answer:

[tex] \sf {\underline{2 \sqrt{5} }}[/tex]

Explaination :

[tex] \sf \: \angle FDE \: = 90 \degree \\ \sf \: by \: pythagoras \: theoram \\ \sf {6}^{2} = {y}^{2} + {4}^{2} \\ \sf{y}^{2} = {6}^{2} - {4}^{2} \\ \sf {y}^{2} = 36 - 16 \\ \sf{y}^{2} = 20 \\ \sf \: y = \sqrt{20} = \sqrt{4 \times 5} = 2 \sqrt{5} [/tex]

The value of y in the triangle is 2√5

The triangle above is a right angle triangle.

Characteristics of a right angle triangle:

  • One of its angle is equals to 90 degrees
  • The sides can be found using Pythagoras theorem.

Using Pythagoras theorem

  • c² = a² + b²

where

c = hypotenuse(longest side)

a and b are the 2 other legs.

Therefore,

6² = 4² + y²

36 = 16 + y²

y² = 36 - 16

y² = 20

y = √20

y = 2√5

learn more on right angle triangle here:https://brainly.com/question/3770177?referrer=searchResults

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